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Physical Review A

Detection efficiency in the loophole-free violation of Svetlichny's inequality

Yang Xiang, Huixian Wang, Fang-Yu Hong

Published Sep 17, 2012• 4 citations
Publisher

Abstract

Svetlichny's inequality (SI) is a Bell-like inequality, the violation of which can be used to confirm the existence of genuine multipartite correlations. However, poor detector efficiency can possibly cause a so-called detection loophole in actual Svetlichny experiments. We derive an alternative SI to deal with this loophole. If the experimental data can violate this SI, it must result in loophole-free violation of the original SI. We show that the minimum detection efficiency needed for a loophole-free violation of the tripartite SI is about $0.97$. For the general case of $n$ particles, we give the analytic expression of the needed detection efficiency, and find that its value monotonically and rapidly approaches 1 as the number of particles increases.

DOI
10.1103/physreva.86.034102

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Svetlichny's inequality (SI) is a Bell-like inequality, the violation of which can be used to confirm the existence of genuine multipartite correlations. However, poor detector efficiency can possibly cause a so-called detection loophole in actual Svetlichny experiments. We derive an alternative SI to deal with this loophole. If the experimental data can violate this SI, it must result in loophole-free violation of the original SI. We show that the minimum detection efficiency needed for a loophole-free violation of the tripartite SI is about 0.970.970.97. For the general case of nnn particles, we give the analytic expression of the needed detection efficiency, and find that its value monotonically and rapidly approaches 1 as the number of particles increases.
In many quantum information applications, a minimum detection efficiency must be exceeded to ensure success. Protocols depending on the violation of a Bell inequality, for instance, may be subject to the so-called detection loophole: Imperfect detectors may yield spurious violations, which consequently cannot be used to ensure, say, quantum cryptographic security. Hence, we investigate the possibility of giving lower bounds on detector efficiency even if an adversary has full control over both the source and the detectors. To this end, we present a technique to systematically derive Bell inequalities free from the detection loophole using only the observed measurements statistics. The violation of these inequalities certifies that the detectors used exceed a certain minimal efficiency.
The certification of quantum nonlocality, which has immense significance in designing device-independent technologies, confronts severe experimental challenges. Detection loopholes, originating from the unavailability of perfect detectors, are one of the major issues among them. In the present study we focus on the minimum detection efficiency (MDE) required to detect various forms of genuine nonlocality, originating from the type of causal constraints imposed on the involved parties. In this context, we demonstrate that the MDE needed to manifest the recently suggested T2{T}_{2}T2​-type nonlocality deviates significantly from perfection. Additionally, we have computed the MDE necessary to manifest Svetlichny's nonlocality, with the state-independent approach markedly reducing the previously established bound. Finally, considering the inevitable existence of noise we demonstrate the robustness of the imperfect detectors to certify T2{T}_{2}T2​-type nonlocality.
Klyachko–Can–Binicioglu–Shumovsky (KCBS) inequality is a Bell-like inequality,the violation of which can be used to confirm the existence of quantum contextuality.However,the imperfection of detection efficiency may cause the so-called loophole in actual KCBS’s experiments.We derive an alternative KCBS inequality to deal with the loophole in actual KCBS’s experiments.We prove that if the experimental data violate this KCBS inequality,the loophole-free violation of the original KCBS inequality will occur.We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.
The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.
Klyachko—Can—Binicioğlu—Shumovsky (KCBS) inequality is a Bell-like inequality, the violation of which can be used to confirm the existence of quantum contextuality. However, the imperfection of detection efficiency may cause the so-called loophole in actual KCBS's experiments. We derive an alternative KCBS inequality to deal with the loophole in actual KCBS's experiments. We prove that if the experimental data violate this KCBS inequality, the loophole-free violation of the original KCBS inequality will occur. We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.
The phenomenon of superactivation of quantum nonlocality, i.e., the fact that several copies of a local quantum state when processed together can generate nonlocal correlations, has recently attracted much attention. However, this problem was considered mainly in a bipartite scenario (although some research in a multipartite case was also undertaken). In this paper we give explicit examples of activation of the violation of the Svetlichny inequality. The violation of the Svetlichny inequality is a sufficient condition of genuine tripartite nonlocality. We show that a number of pure GHZ-type states can be activated. We observe also that the amount of violation of the Svetlichny inequality by two copies of the GHZ state increases with an entanglement of a single copy of the state.